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501
Injectivity Radius of Lorentzian Manifolds
 COMMUN. MATH. PHYS.
, 2007
"... Motivated by the application to general relativity we study the geometry and regularity of Lorentzian manifolds under natural curvature and volume bounds, and we establish several injectivity radius estimates at a point or on the past null cone of a point. Our estimates are entirely local and geome ..."
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Cited by 7 (1 self)
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Motivated by the application to general relativity we study the geometry and regularity of Lorentzian manifolds under natural curvature and volume bounds, and we establish several injectivity radius estimates at a point or on the past null cone of a point. Our estimates are entirely local
Injectivity radius estimates and sphere theorems
 Comparison Geometry, MSRI Publications
, 1997
"... Abstract. We survey results about the injectivity radius and sphere theorems, from the early versions of the topological sphere theorem to the authors ’ most recent pinching below 1 theorems, explaining at each stage 4 the new ideas involved. ..."
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Cited by 8 (0 self)
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Abstract. We survey results about the injectivity radius and sphere theorems, from the early versions of the topological sphere theorem to the authors ’ most recent pinching below 1 theorems, explaining at each stage 4 the new ideas involved.
THE MAXIMUM INJECTIVITY RADIUS OF HYPERBOLIC ORBIFOLDS
"... Abstract. For twodimensional orientable hyperbolic orbifolds, we show that the radius of a maximal embedded disk is greater or equal to an explicit constant ρT, with equality if and only if the orbifold is a sphere with three cone points of order 2, 3 and 7. 1. ..."
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Abstract. For twodimensional orientable hyperbolic orbifolds, we show that the radius of a maximal embedded disk is greater or equal to an explicit constant ρT, with equality if and only if the orbifold is a sphere with three cone points of order 2, 3 and 7. 1.
Injectivity radius and fundamental groups of hyperbolic 3manifolds
 Comm. Anal. Geom
"... Abstract. It is shown that for each integer n> 1 there exists a constant Rn> 0 such that if M is a closed hyperbolic 3manifold with Rank π1(M) = n, then the injectivity radius of M is bounded above by Rn. 1. ..."
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Cited by 16 (2 self)
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Abstract. It is shown that for each integer n> 1 there exists a constant Rn> 0 such that if M is a closed hyperbolic 3manifold with Rank π1(M) = n, then the injectivity radius of M is bounded above by Rn. 1.
ON THE INJECTIVITY RADIUS OF HYPERBOLIC POLYHEDRA AND RATIONAL HOMOLOGY SPHERES
, 1998
"... Abstract. We define the injectivity radius of a Coxeter polyhedron in H 3 to be half the shortest translation length among hyperbolic/loxodromic elements in the orientationpreserving reflection group. We show that, for finitevolume polyhedra, this number is always less than 2.6339..., and for comp ..."
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Abstract. We define the injectivity radius of a Coxeter polyhedron in H 3 to be half the shortest translation length among hyperbolic/loxodromic elements in the orientationpreserving reflection group. We show that, for finitevolume polyhedra, this number is always less than 2
Injectivity radius bounds in hyperbolic convex cores
, 1997
"... Abstract. A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3manifold homeomorphic to the interior of M, then the injectivity radius based at points in the convex co ..."
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Cited by 3 (0 self)
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Abstract. A version of a conjecture of McMullen is as follows: Given a hyperbolizable 3manifold M with incompressible boundary, there exists a uniform constant K such that if N is a hyperbolic 3manifold homeomorphic to the interior of M, then the injectivity radius based at points in the convex
Injectivity Radius of Representations of Triangle Groups and Planar Width of Regular Hypermaps
, 2008
"... and other research outputs Injectivity radius of representations of triangle groups and planar width of regular hypermaps Journal Article ..."
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Cited by 1 (0 self)
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and other research outputs Injectivity radius of representations of triangle groups and planar width of regular hypermaps Journal Article
Injectivity Radius of Representations of Triangle Groups and Planar Width of Regular Hypermaps
, 2008
"... and other research outputs Injectivity radius of representations of triangle groups and planar width of regular hypermaps Journal Article ..."
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and other research outputs Injectivity radius of representations of triangle groups and planar width of regular hypermaps Journal Article
Curvature and injectivity radius estimates for Einstein 4manifolds
 J. Amer. Math. Soc
"... It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2dimensional Einstein manifold, (M2, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1 ..."
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Cited by 31 (2 self)
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It is of fundamental interest to study the geometric and analytic properties of compact Einstein manifolds and their moduli. In dimension 2 these problems are well understood. A 2dimensional Einstein manifold, (M2, g), has constant curvature, which after normalization, can be taken to be −1, 0 or 1. Thus, (M2, g) is the quotient of a space form and the metric, g, is completely determined by the conformal structure. For fixed M2, the moduli space of all such g admits a natural compactification, the DeligneMumford compactification, which has played a crucial role in geometry and topology in the last two decades, e.g. in establishing GromovWitten theory in symplectic and algebraic geometry. In dimension 3, it remains true that Einstein manifolds have constant sectional curvature and hence are quotients of space forms. An essential portion of Thurston’s geometrization program can be viewed as the problem of determining which 3manifolds admit Einstein metrics. The moduli space of Einstein metrics on a 3dimensional manifold is also well understood. As a consequence of Mostow rigidity, the situation is actually simpler than in twodimensions.
Homomorphisms of triangle groups with large injectivity radius
 Acta Math. Univ. Comenianae
"... Abstract. We prove a new upper bound on the smallest order o(l,m, n; r) of a finite group that is a homomorphic image of a triangle group T (l,m, n) with injectivity radius at least r. 1. ..."
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Abstract. We prove a new upper bound on the smallest order o(l,m, n; r) of a finite group that is a homomorphic image of a triangle group T (l,m, n) with injectivity radius at least r. 1.
Results 1  10
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501